Monte Carlo study of the domain kinetics of the Ising model with random coupling constants

Effect of bond-disorder on the phase-separation kinetics of binary mixtures: A Monte Carlo simulation study

We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For a higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov power-law growth in all the cases.

Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration

We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction a of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of a, a<a_{f}. In an intermediate range, a_{f}<a<a_{a}, the system is paramagnetic, with spin-glass order expected right at zero temperature. For even larger values, a>a_{a}, an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of a. We show that different amounts of frustration, tuned by a, affect the dynamical properties in a highly nontrivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e., algebraic, when spin-glass order is prevailing. An interpretation is given in terms of the different nature of phase space.

Coarsening and percolation in a disordered ferromagnet

By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework.

Relaxation dynamics of an elastic string in random media

We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the correlation length grows in time asymptotically as xi approximately (ln t)1/chi . This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as EB(l) approximately l;chi with a length scale l . Numerical data strongly suggest that the energy barrier exponent chi is identical to the energy fluctuation exponent chi=1/3 . We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as xi approximately t1/z with a nonuniversal dynamic exponent z . The origin of the transient scaling behavior is discussed in the context of the relaxation dynamics on finite ramified clusters of disorder.

Domain growth in Ising systems with quenched disorder

We present results from extensive Monte Carlo (MC) simulations of domain growth in ferromagnets and binary mixtures with quenched disorder. These are modeled by the random-bond Ising model and the dilute Ising model with either nonconserved (Glauber) spin-flip kinetics or conserved (Kawasaki) spin-exchange kinetics. In all cases, our MC results are consistent with power-law growth with an exponent theta(T, epsilon) which depends on the quench temperature T and the disorder amplitude epsilon. Such exponents arise naturally when the coarsening domains are trapped by energy barriers that grow logarithmically with the domain size. Our MC results show excellent agreement with the predicted dependence of theta(T, epsilon).